This is the fourth, but not necessarily the last, unexpurgated volume of Alastair Campbell's diaries. It covers the period from 9/11 to the day, two fraught years later, when he finally leaves Downing Street. Two issues predominate: the increasingly dysfunctional relationship between the two most powerful men in the government, and Iraq – the buildup to the invasion and then the fallout. By the end, Iraq eclipses everything. This volume is of interest, too, for the light it sheds on the pressures of life at the top of government and the fractious relationship between politicians and a 24-hour media hungry for sensation.

On Iraq there is little new. Those from the "Blair is a liar" school of political history will find nothing here for their comfort. Campbell offers an insider's account of just about all the crucial meetings, and there is nothing to suggest that anyone knew Saddam did not still possess chemical or biological weapons. The consistent advice offered to ministers by the spooks was that he did. No sooner has Iraq been "liberated", however, than the spooks begin to have second thoughts. Five weeks after the invasion Campbell reports a phone call from the head of MI6, John Scarlett, who asks with touching naivety: "How big a problem would it be if we didn't find any [WMD]?" Now they tell us. The bottom line is that Iraq was an intelligence screw-up. In the circumstances, the spooks got off remarkably lightly.

There is evidence for the proposition that Blair was extraordinarily reckless in throwing in his lot with George W Bush and his cronies. As one of his close allies remarked to me at the time: "He's bet the whole shop." Blair's strategy, post 9/11, was to get in close to the Americans and attempt to influence them from the inside. Initially, he had some success. He did persuade Bush to overrule Cheney and Rumsfeld and take the American case to the United Nations. Gradually, however, he got sucked in, and the rest is history.

As for the relationship between the prime minister and his chancellor, Gordon Brown, Campbell has much to offer. This was the great faultline running through the New Labour administration, and few outside the inner circle knew quite how bad the situation was. No sooner is the 2001 election out of the way than Brown is demanding to know when Blair will stand aside. By November, Campbell writes: "TB/GB relations so bad that it was currently almost impossible to get either of them to say a good word about the other."

To the consternation of other ministers, Brown was always interfering in their departments, at one stage even proposing to announce a review of health policy without so much as consulting the health secretary, Alan Milburn – who was, unsurprisingly, incandescent. By May 2002, Blair was accusing Brown of waging a war of attrition: "He wants me out and thinks he has to wear me out to get me out." "He's like a lover spurned," John Prescott remarked after listening to one of Brown's outbursts. "Has he got something on you?" an exasperated Jack Straw asked. "How else do we explain to ourselves why you tolerate it?" "It's like watching a marriage fall apart," Jonathan Powell, Blair's chief of staff, said.

Brown's shadow hangs over things like a great black cloud. Several times Blair is said to be at the end of his tether. More than once he talks of surrender ("I've never wanted to do more than two terms anyway …"). More than once he makes up his mind to sack or reshuffle Brown but always backs off, knowing the chaos this would cause. Even at the worst of times, though, Blair appears mesmerised by Brown's alleged brilliance. There is much talk, prompted perhaps by guilt at having overtaken him at the final hurdle in the leadership race, of Brown's towering intellect, and that at his best he is head and shoulders above everyone else. Towards the end, however, doubts begin to creep in as to whether Brown is actually fitted for office. By then, of course, it is too late.

There is, however, one large crumb of comfort for anyone in search of a reason to be grateful to Brown: he kept the UK out of the euro. Blair was keen that Britain should join but Brown, with his five unmeetable tests, was opposed. Or could it be that he was against it simply because Blair was in favour? Or because he needed to keep in with his friends at the Mail and the Sun and that, given half a chance, once safely installed at No 10, he intended to take us in anyway? With Brown, you could never tell.

Campbell's relationship with Blair is one of equals. He never hesitates to tell his master what he doesn't want to hear and is forever mocking Blair for his eccentric dress sense ("I said what a prat he looked"). Media feeding frenzies come and go. Carole Caplin, Cherie Blair's supposed "lifestyle guru", who featured in earlier volumes, resurfaces with a vengeance – her dodgy boyfriend appears to have been representing himself as Cherie's financial adviser. Campbell has been warning from the outset that the association with Caplin is trouble with a capital T, but the Blairs refuse to listen and it is the source of considerably tension ("Why the fuck should I spend so much of my life digging them out of shit of their own making?"). No sooner has one frenzy died down than a new one flares up. My favourite is the – false – suggestion that Blair had tried to manoeuvre himself a more prominent role in the Queen Mother's funeral. It raged for days and then disappeared as though someone had flicked off a switch.

And in the middle of it all, there's one prescient sentence: "Both Fiona [Campbell's partner] and Godric [Smith, his deputy] were of the view that some of us were being bugged by someone flogging stuff to the media or by the media per se. It was extraordinary how many private conversations were getting out." Note the date: Thursday 19 June 2003, eight years before the News of the World was shown to have bugged Milly Dowler's phone. A bullseye.

This is not an easy read. As in earlier volumes, the pace of events is so relentless that it is hard for ordinary mortals to keep pace as a small elite flit between capital cities and fortified condominiums – and to complicate matters, most participants are referred to by their initials. Campbell comes into his own, however, when the big events take over. The final months leading to the Hutton inquiry into the circumstances leading to the death of David Kelly are riveting.

Campbell himself comes across as a flawed genius, more spinned against than spinning (in my experience, political journalists are far greater spinners than politicians or their spokesmen – it is sometimes necessary to run one's finger down several inches of interpretation before coming to the sliver of fact that justifies a sensational headline). He is a man of excellent strategic and tactical judgment (it is easy to see why Blair became so dependent upon him), brutally honest, occasionally self-indulgent and jealous of his undoubted integrity; a man of obsessive hatreds (Clare Short, the Daily Mail and ultimately the BBC), but also a man with a hinterland (marathon runner, bagpipe player, supporter of Burnley Football Club).

By the end, with accusations flying about dodgy dossiers and Kelly's death, Campbell has become the story – never a good position for an official spokesman. By this point our hero is living under a virtual state of siege, under pressure on all fronts and reduced to clambering over fences in neighbouring back gardens in order to avoid the press pack at his front door, desperate to leave No 10 and yet unable to do so for fear of appearing to run away. Reading all this, one can't help wondering whether there is a better way of governing. Is this how it must always be in the age of the 24/7 media? Might it have been easier for all concerned if there has been less control-freakery? If instead of trying to ride the media tiger, New Labour had kept its distance?

• Chris Mullin's A Walk-On Part, the third and final volume of his diaries as a Labour minister, is published by Profile Books.